Gamow's Order free overlapping code

How it worked and gave 20 amino acids

Gamow’s order free overlapping code: Gamow suggested yet another overlapping-triplet code with an even simpler description: Each codon is defined entirely by its base composition, ignoring the order of the bases within the codon. In other words, any reordering of the three nucleotides does not change the codon. Thus ACT, ATC, CAT, CTA, TAC and TCA are equivalent and specify the same amino acid. Show that the number of codon families in this scheme again turns out to be exactly 20.

Solution: If the codon is defined only by its nucleotide base composition, then with 4 bases A, C, G, T, one possible combination are the ones in the set, where we eliminate all permutations for each codon.

S = {AAA, CCC, GGG, TTT, AAC, AAG, AAT, CCA, CCG, CCT, GGA,

GGC, GGT, TTA, TTC, TTG, ACG, ACT, AGT, CGT}.

We see that the set S has exactly 20 members. A permutation of nucleotides within each of these codons represents the same amino acid.